Cut peppers into halves crosswise and remove seeds and white membrane. Cook peppers in 2 cups of boiling water for 4 minutes. Drain and reserve liquid. Cook rice until tender; drain. In a skillet, sauté onion in butter until onion is tender, about 4 to 5 minutes.

Add 3/4 cup water and shredded cheese. Stir until blended; add ham, rice, parsley, salt, and pepper. Fill pepper halves with rice and ham mixture; put on rack in skillet with about 1 1/2 cups of the pepper cooking liquid in the bottom. Cover and simmer over low heat for 15 to 20 minutes.